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Table of Contents

Chapter 1: Introduction
1.1 Background of the Study
1.2 Statement of the Problem
1.3 Objective of the Study
1.4 Limitation of the Study
1.5 Scope of the Study

Chapter 2: Literature Review
2.1 Introduction to Carnot Groups
2.2 Geometric Measure Theory
2.3 Previous Studies on Geometric measure theory in Carnot groups

Chapter 3: Research Methodology
3.1 Research Design
3.2 Data Collection Methods
3.3 Data Analysis Techniques

Chapter 4: Discussion of Findings
4.1 Analysis of Results
4.2 Interpretation of Findings
4.3 Implications of the Findings

Chapter 5: Conclusion and Summary
5.1 Summary of the Study
5.2 Conclusion
5.3 Recommendations for Future Research

Brief Overview:

Geometric measure theory in Carnot groups is a complex and specialized field of mathematics that involves the study of geometric properties of sets and functions in Carnot groups. Carnot groups are a class of non-commutative Lie groups with a distinguished family of subgroups.

Geometric measure theory is concerned with the study of geometric objects such as curves, surfaces, and volumes, and their measure-theoretic properties. The theory has applications in various fields, including differential geometry, harmonic analysis, and partial differential equations.

This thesis aims to explore the applications of geometric measure theory in Carnot groups, including the study of tangent spaces, Hausdorff measures, and rectifiable sets. The research methodology involves a review of existing literature on the topic, as well as the development of new results and techniques.

The findings of this thesis are expected to contribute to the existing body of knowledge in the field of geometric measure theory in Carnot groups and provide insights for future research in the area. The conclusion and summary will highlight the key findings and implications of the study.

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